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In her resignation letter, Caulfield warned that May's policy "may assuage vested interests, but the voters will find out and their representatives will be found out".

"This policy will be bad for our country and bad for the party," said the Lewes MP. "The direct consequences of that will be Prime Minister Corbyn."

Bradley said that the Brexit plan agreed by the Cabinet last week at Chequers would damage the UK's opportunities to develop global trade and be "an outward-looking nation in control of our own destiny" following Brexit.

"Being tied to EU regulations and the EU tying our hands when seeking to make new trade agreements will be the worst of all worlds," wrote the Mansfield MP, who voted remain in a constituency where more than 70% of voters opted to leave.

"If we do not deliver Brexit in spirit as well as in name, then we are handing Jeremy Corbyn the keys to Number 10."

Conservative chairman Brandon Lewis said: "Maria Caulfield and Ben Bradley have worked hard since the start of the year to promote women and young people on behalf of the Conservative Party.

"I wish them both well as they return to the backbenches to serve their constituents."

Maria Caulfield MP also quit as Conservative vice-chair in a fresh batch of resignations (Image: PA)

Labour MP Owen Smith, a supporter of the Best for Britain campaign for a second EU referendum, said: "David Davis and the other resigning Tories are just the first of the rats to quit the sinking Brexit ship.

"They lied to the country about the benefits of Brexit and they are now running away from any responsibility for the harm it is set to do our economy.

"We need a vote for the people on the final Brexit deal and an opportunity for us all to flee this disaster."

And a Labour source said: "With just weeks to go to negotiate Brexit, NHS waiting lists growing and pay packets being squeezed, the Conservative Party continues to tear itself apart. Something has got to give."

Earlier in the day, May was bolstered by the support of senior Brexiteers in her Cabinet.

Michael Gove left no doubt that he would not follow Boris Johnson and David Davis out of the Cabinet, declaring that he backed the Prime Minister's plans "100%".

And International Trade Secretary Liam Fox was seen to shake his head and mouth the word "No" when reporters asked him on his way out of Cabinet whether he was about to quit.

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Jeremy Hunt, appointed the new Foreign Secretary as the Prime Minister carried out a hurried reshuffle of her top team, vowed that he would be "four square" behind her in driving through her Brexit plan.

Gove told ITV News he was "absolutely not" planning to resign.

Asked whether May was in trouble following the rash of departures from her Government on Monday, the Environment Secretary replied: "No."

In a tweet clearly designed to show she was not being knocked off course, May said: "Productive Cabinet meeting this morning - looking ahead to a busy week. And sending our best wishes to @England for tomorrow!"

The PM's official spokesman later said that Cabinet gave its approval to pressing ahead with preparations for a possible "no deal" Brexit as agreed at Chequers last Friday.

New Brexit Secretary Dominic Raab chaired a meeting with business leaders to discuss the Chequers plan, which would see the UK agree to follow a "common rulebook" on trade with the EU in goods but accept restricted access for services.

Among Tory Brexiteers there was deepening anger at the proposals agreed by the Cabinet at Chequers, which they branded "Brexit in name only".

However it was unclear whether they had the numbers to force a leadership challenge.

Under party rules, 48 Tory MPs - 15% of the party's 316-strong representation in the Commons - must write to the chairman of the backbench 1922 Committee, Sir Graham Brady, to trigger a no-confidence vote.

Former leader Lord Howard said a bid to oust May would be "extremely foolish and extremely ill-advised".

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After Johnson posed for press photos signing his own resignation letter, Labour's deputy leader Tom Watson said he clearly had "a career ahead of him on Love Yourself Island".

Watson said Labour was keeping the option of a second Brexit referendum open in the case that Parliament could not decide a way forward, though he stressed that this route was "highly, highly unlikely".

Meanwhile, Justice Secretary David Gauke warned Tory Eurosceptics that a "no-deal" Brexit was "not an attractive option at all".

While insisting that the option cannot be ruled out, Gauke told Today: "What I would say to those of my colleagues, if there are some, who think this is pain-free and this is just something that we can ride over very easily, is no deal will have a negative impact on our constituents, on the British public."

Brexiteers' anger was fuelled by the fact that Monday's rapid reshuffle leaves the four great offices of state - Prime Minister, Chancellor, Foreign Secretary and Home Secretary - in the hands of ministers who voted to stay in the EU.